Convergence Analysis of a Randomized Incremental Subgradient Method on Riemannian Manifolds

This study presents and examines a randomized incremental subgradient algorithm designed to tackle convex optimization problems on Riemannian manifolds. The objective function comprises multiple constituent functions, necessitating specialized computational strategies. Our approach adapts the randomized incremental subgradient method from Euclidean spaces to the context of Riemannian manifolds. By assuming non-negative sectional curvature within the Riemannian manifolds, we rigorously establish convergence properties through both fixed and diminishing step size strategies.